Select all of the ordered pairs that are solutions to the following system of inequalities. -5x+y<8
5x>4y-6
a. 0,0
b. -1,-6
c.8,4
d.-1,3
To determine which ordered pairs are solutions to the system of inequalities, we need to test each pair by substituting the x and y values into each inequality and see if they are true statements.
For a: (0,0)
-5(0) + 0 < 8
0 < 8 (True)
5(0) > 4(0) - 6
0 > -6 (True)
(0,0) is a solution to the system of inequalities.
For b: (-1,-6)
-5(-1) + (-6) < 8
5 - 6 < 8
-1 < 8 (True)
5(-1) > 4(-6) - 6
-5 > -24 (True)
(-1,-6) is a solution to the system of inequalities.
For c: (8,4)
-5(8) + 4 < 8
-40 + 4 < 8
-36 < 8 (True)
5(8) > 4(4) - 6
40 > 10 (True)
(8,4) is a solution to the system of inequalities.
For d: (-1,3)
-5(-1) + 3 < 8
5 + 3 < 8
8 < 8 (False)
5(-1) > 4(3) - 6
-5 > 6 (False)
(-1,3) is not a solution to the system of inequalities.
Therefore, the ordered pairs that are solutions to the system of inequalities are:
a. 0,0
b. -1,-6
c. 8,4